and Strength of Materials. 281 
Its section will then be a circle, fig. 9, in 
which ABC may be supposed to be the area 
of tension, and ABD that of compression, 
the neutral line having been found by Art. 33. 
And if G be the centre of gravity of ABC, 
and P and P” the centres of Sain of 
ABC and ABD, the formula “*2+?) 
+ BG) x ree ABO P ce ze and PP’ 
are unknown quantities; and to find them 
(retaining the previous notation and calling 
the radius OI = r, and AE, £ the neutral line, 
becomes 
AE)3 , 
=b), we have OG = ea (Dealtry’s 
Fluxions, Article 64, Ex. 6th) = ee 
= — And siniee OE — r—a, .. EG = OG 
: att (a—r)A 
SOR 2:2" 4 @-a) = 2 Se. 
And now as finding the distances EP and 
EP’ is attended with too much labour for 
practical purposes, we shall adopt the fol- 
lowing approximation. Let P be the dis- 
tance of the centre of percussion of the semi- 
circle HIC or HID from the centre O, then 
EP will be less, and EP’ greater, than P. 
But as it appears from experiment that AB 
during moderate strains is near to HI, the 
excess must be very nearly equal to the de- 
fect, or EP+EP’ very nearly = 2 P; assum- 
Nn 
